(Four) Dual Plaquette 3D Ising Models.

Abstract

A characteristic feature of the plaquette Ising model is its planar subsystem symmetry. The quantum version of this model has been shown to be related via a duality to the X-Cube model, which has been paradigmatic in the new and rapidly developing field of fractons. The relation between the plaquette Ising and the X-Cube model is similar to that between the quantum transverse spin Ising model and the Toric Code. Gauging the global symmetry in the case of the Ising model and considering the gauge invariant sector of the high temperature phase leads to the Toric Code, whereas gauging the subsystem symmetry of the quantum transverse spin plaquette Ising model leads to the X-Cube model. A non-standard dual formulation of the plaquette Ising model which utilises three flavours of spins has recently been discussed in the context of dualising the fracton-free sector of the X-Cube model. In this paper we investigate the classical spin version of this non-standard dual Hamiltonian and discuss its properties in relation to the more familiar Ashkin–Teller-like dual and further related dual formulations involving both link and vertex spins and non-Ising spins.